The following result proved by Penttila and Van de Voorde [1]} strengthens a result by Casse, Thas, and Wild [2]}.
A conic in a projective plane \(\textnormal {PG}(2,q)\)  is a set of points satisfying an irreducible homogeneous quadratic equation.
All conics are projectively equivalent, and Segre [3]} proved that the largest arcs in \(\textnormal {PG}(2,q)\) , \(q\)  odd, are exactly the conics, which have \(q+1\)  points.
